[R] How are interaction terms computed in lm's result / problems with interaction terms in lm?

[mviljamaa]

> On Sep 18, 2016, at 11:01 AM, mviljamaa <mviljamaa at kapsi.fi> wrote:
> 
> Also if you, rather than doing what's done below, do:
> 
> fit3 <- lm(kidmomhsage$kid_score ~ kidmomhsage$mom_age + 
> kidmomhsage$mom_hs + kidmomhsage$mom_age * kidmomhsage$mom_hs)
> 
> Then this gives the result:
> 
> Call:
> lm(formula = kidmomhsage$kid_score ~ kidmomhsage$mom_age + 
> kidmomhsage$mom_hs +
>    kidmomhsage$mom_age * kidmomhsage$mom_hs)
> 
> Coefficients:
>                           (Intercept)
>                               110.542
>                   kidmomhsage$mom_age
>                                -1.522
>                    kidmomhsage$mom_hs
>                               -41.287
> kidmomhsage$mom_age:kidmomhsage$mom_hs
>                                 2.391
> 
> Where the interaction term now seems properly interpretable. So perhaps 
> this is the way to use interaction terms with lm.

But why does

fit3 <- lm(kidmomhsage$kid_score ~ kidmomhsage$mom_age * 
kidmomhsage$mom_hs)

also give exactly the same result:

Call:
lm(formula = kidmomhsage$kid_score ~ kidmomhsage$mom_age * 
kidmomhsage$mom_hs)

Coefficients:
                            (Intercept)
                                110.542
                    kidmomhsage$mom_age
                                 -1.522
                     kidmomhsage$mom_hs
                                -41.287
kidmomhsage$mom_age:kidmomhsage$mom_hs
                                  2.391

It's as if lm is interpreting there having to also be "independent" 
mom_age and mom_hs variables, if there's just the interaction term. Why 
does it work this way?